Patient number % reticulocytes Lymphocytes (per mm 2 ) 1 3.6 1700 2 2.0 3078 3 0
ID: 3126469 • Letter: P
Question
Patient number
% reticulocytes
Lymphocytes (per mm2)
1
3.6
1700
2
2.0
3078
3
0.3
1820
4
0.3
2708
5
0.2
2086
6
3.0
2299
7
0.0
676
8
1.0
2088
9
2.2
2013
Use Stata to answer the following questions.
a. Fit a regression line relating the percentage of reticulocytes (x) to the number of lymphocytes (y).
b. Test for the statistical significance of this regression line using the F test.
c. What is R2 for the regression line in (a)?
d. What does R2 mean in (c)?
e. What is s2y.x?
f. Test for the statistical significance of the regression line using the t test.
g. What are the standard errors of the slope and intercept for the regression line in (a)?
Patient number
% reticulocytes
Lymphocytes (per mm2)
1
3.6
1700
2
2.0
3078
3
0.3
1820
4
0.3
2708
5
0.2
2086
6
3.0
2299
7
0.0
676
8
1.0
2088
9
2.2
2013
Explanation / Answer
Let independent variable x be % reticulocytes.
and dependent variable y be the number of lymphocytes.
Assume alpha = level of significance = 5% = 0.05
All the questions we are done by using MINITAB.
Steps :
Enter data in MINITAB sheet --> Stat --> Regression --> Regression --> Response : y --> Predictors : x --> Results --> select second option --> ok --> ok
Output :
Regression Analysis: y versus x
The regression equation is
y = 1895 + 112 x
Predictor Coef SE Coef T P
Constant 1895.3 348.6 5.44 0.001
x 112.0 184.8 0.61 0.564
S = 700.902 R-Sq = 5.0% R-Sq(adj) = 0.0%
Analysis of Variance
Source DF SS MS F P
Regression 1 180257 180257 0.37 0.564
Residual Error 7 3438841 491263
Total 8 3619098
a. Fit a regression line relating the percentage of reticulocytes (x) to the number of lymphocytes (y).
The regression line is,
y = 1895 + 112 x
b. Test for the statistical significance of this regression line using the F test.
Here test of hypothesis is,
H0 : B = 0 Vs H1 : B 0
where B is the population slope for percentage of reticulocytes.
We see that P-value for F test is 0.564
P-value > alpha
Accept H0 at 5% level of significance.
Conclusion : Population slope for for percentage of reticulocytes is 0.
c. What is R2 for the regression line in (a)?
R2 in a regression line is 5.0%.
d. What does R2 mean in (c)?
Interpretation : R2 = 5.0% expresses the proportion of the variation in the number of lymphocytes which is explained by variation in % reticulocytes.
e. What is s2y.x?
s2y.x = 700.902
f. Test for the statistical significance of the regression line using the t test.
This part has same answer as part b).
g. What are the standard errors of the slope and intercept for the regression line in (a)?
Standard error for intercept is 348.6
Standard error for slope is 184.8.